1 2 /* 3 * Copyright 2006 The Android Open Source Project 4 * 5 * Use of this source code is governed by a BSD-style license that can be 6 * found in the LICENSE file. 7 */ 8 9 10 #ifndef SkMath_DEFINED 11 #define SkMath_DEFINED 12 13 #include "SkTypes.h" 14 15 //! Returns the number of leading zero bits (0...32) 16 int SkCLZ_portable(uint32_t); 17 18 /** Computes the 64bit product of a * b, and then shifts the answer down by 19 shift bits, returning the low 32bits. shift must be [0..63] 20 e.g. to perform a fixedmul, call SkMulShift(a, b, 16) 21 */ 22 int32_t SkMulShift(int32_t a, int32_t b, unsigned shift); 23 24 /** Computes numer1 * numer2 / denom in full 64 intermediate precision. 25 It is an error for denom to be 0. There is no special handling if 26 the result overflows 32bits. 27 */ 28 int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom); 29 30 /** Computes (numer1 << shift) / denom in full 64 intermediate precision. 31 It is an error for denom to be 0. There is no special handling if 32 the result overflows 32bits. 33 */ 34 int32_t SkDivBits(int32_t numer, int32_t denom, int shift); 35 36 /** Return the integer square root of value, with a bias of bitBias 37 */ 38 int32_t SkSqrtBits(int32_t value, int bitBias); 39 40 /** Return the integer square root of n, treated as a SkFixed (16.16) 41 */ 42 #define SkSqrt32(n) SkSqrtBits(n, 15) 43 44 /** Return the integer cube root of value, with a bias of bitBias 45 */ 46 int32_t SkCubeRootBits(int32_t value, int bitBias); 47 48 /** Returns -1 if n < 0, else returns 0 49 */ 50 #define SkExtractSign(n) ((int32_t)(n) >> 31) 51 52 /** If sign == -1, returns -n, else sign must be 0, and returns n. 53 Typically used in conjunction with SkExtractSign(). 54 */ 55 static inline int32_t SkApplySign(int32_t n, int32_t sign) { 56 SkASSERT(sign == 0 || sign == -1); 57 return (n ^ sign) - sign; 58 } 59 60 /** Return x with the sign of y */ 61 static inline int32_t SkCopySign32(int32_t x, int32_t y) { 62 return SkApplySign(x, SkExtractSign(x ^ y)); 63 } 64 65 /** Returns (value < 0 ? 0 : value) efficiently (i.e. no compares or branches) 66 */ 67 static inline int SkClampPos(int value) { 68 return value & ~(value >> 31); 69 } 70 71 /** Given an integer and a positive (max) integer, return the value 72 pinned against 0 and max, inclusive. 73 @param value The value we want returned pinned between [0...max] 74 @param max The positive max value 75 @return 0 if value < 0, max if value > max, else value 76 */ 77 static inline int SkClampMax(int value, int max) { 78 // ensure that max is positive 79 SkASSERT(max >= 0); 80 if (value < 0) { 81 value = 0; 82 } 83 if (value > max) { 84 value = max; 85 } 86 return value; 87 } 88 89 /** Given a positive value and a positive max, return the value 90 pinned against max. 91 Note: only works as long as max - value doesn't wrap around 92 @return max if value >= max, else value 93 */ 94 static inline unsigned SkClampUMax(unsigned value, unsigned max) { 95 #ifdef SK_CPU_HAS_CONDITIONAL_INSTR 96 if (value > max) { 97 value = max; 98 } 99 return value; 100 #else 101 int diff = max - value; 102 // clear diff if diff is positive 103 diff &= diff >> 31; 104 105 return value + diff; 106 #endif 107 } 108 109 /////////////////////////////////////////////////////////////////////////////// 110 111 #if defined(__arm__) 112 #define SkCLZ(x) __builtin_clz(x) 113 #endif 114 115 #ifndef SkCLZ 116 #define SkCLZ(x) SkCLZ_portable(x) 117 #endif 118 119 /////////////////////////////////////////////////////////////////////////////// 120 121 /** Returns the smallest power-of-2 that is >= the specified value. If value 122 is already a power of 2, then it is returned unchanged. It is undefined 123 if value is <= 0. 124 */ 125 static inline int SkNextPow2(int value) { 126 SkASSERT(value > 0); 127 return 1 << (32 - SkCLZ(value - 1)); 128 } 129 130 /** Returns the log2 of the specified value, were that value to be rounded up 131 to the next power of 2. It is undefined to pass 0. Examples: 132 SkNextLog2(1) -> 0 133 SkNextLog2(2) -> 1 134 SkNextLog2(3) -> 2 135 SkNextLog2(4) -> 2 136 SkNextLog2(5) -> 3 137 */ 138 static inline int SkNextLog2(uint32_t value) { 139 SkASSERT(value != 0); 140 return 32 - SkCLZ(value - 1); 141 } 142 143 /** Returns true if value is a power of 2. Does not explicitly check for 144 value <= 0. 145 */ 146 static inline bool SkIsPow2(int value) { 147 return (value & (value - 1)) == 0; 148 } 149 150 /////////////////////////////////////////////////////////////////////////////// 151 152 /** SkMulS16(a, b) multiplies a * b, but requires that a and b are both int16_t. 153 With this requirement, we can generate faster instructions on some 154 architectures. 155 */ 156 #if defined(__arm__) \ 157 && !defined(__thumb__) \ 158 && !defined(__ARM_ARCH_4T__) \ 159 && !defined(__ARM_ARCH_5T__) 160 static inline int32_t SkMulS16(S16CPU x, S16CPU y) { 161 SkASSERT((int16_t)x == x); 162 SkASSERT((int16_t)y == y); 163 int32_t product; 164 asm("smulbb %0, %1, %2 \n" 165 : "=r"(product) 166 : "r"(x), "r"(y) 167 ); 168 return product; 169 } 170 #else 171 #ifdef SK_DEBUG 172 static inline int32_t SkMulS16(S16CPU x, S16CPU y) { 173 SkASSERT((int16_t)x == x); 174 SkASSERT((int16_t)y == y); 175 return x * y; 176 } 177 #else 178 #define SkMulS16(x, y) ((x) * (y)) 179 #endif 180 #endif 181 182 /** Return a*b/255, truncating away any fractional bits. Only valid if both 183 a and b are 0..255 184 */ 185 static inline U8CPU SkMulDiv255Trunc(U8CPU a, U8CPU b) { 186 SkASSERT((uint8_t)a == a); 187 SkASSERT((uint8_t)b == b); 188 unsigned prod = SkMulS16(a, b) + 1; 189 return (prod + (prod >> 8)) >> 8; 190 } 191 192 /** Return a*b/255, rounding any fractional bits. Only valid if both 193 a and b are 0..255 194 */ 195 static inline U8CPU SkMulDiv255Round(U8CPU a, U8CPU b) { 196 SkASSERT((uint8_t)a == a); 197 SkASSERT((uint8_t)b == b); 198 unsigned prod = SkMulS16(a, b) + 128; 199 return (prod + (prod >> 8)) >> 8; 200 } 201 202 /** Return (a*b)/255, taking the ceiling of any fractional bits. Only valid if 203 both a and b are 0..255. The expected result equals (a * b + 254) / 255. 204 */ 205 static inline U8CPU SkMulDiv255Ceiling(U8CPU a, U8CPU b) { 206 SkASSERT((uint8_t)a == a); 207 SkASSERT((uint8_t)b == b); 208 unsigned prod = SkMulS16(a, b) + 255; 209 return (prod + (prod >> 8)) >> 8; 210 } 211 212 /** Return a*b/((1 << shift) - 1), rounding any fractional bits. 213 Only valid if a and b are unsigned and <= 32767 and shift is > 0 and <= 8 214 */ 215 static inline unsigned SkMul16ShiftRound(unsigned a, unsigned b, int shift) { 216 SkASSERT(a <= 32767); 217 SkASSERT(b <= 32767); 218 SkASSERT(shift > 0 && shift <= 8); 219 unsigned prod = SkMulS16(a, b) + (1 << (shift - 1)); 220 return (prod + (prod >> shift)) >> shift; 221 } 222 223 /** Just the rounding step in SkDiv255Round: round(value / 255) 224 */ 225 static inline unsigned SkDiv255Round(unsigned prod) { 226 prod += 128; 227 return (prod + (prod >> 8)) >> 8; 228 } 229 230 #endif 231 232
